Abstract
Numerical experiments indicate that symmetric methods applied to integrable and near-integrable reversible systems share similar properties to symplectic methods applied to (near-)integrable Hamiltonian systems: linear error growth, long-time near-conservation of first integrals, existence of invariant tori. The present chapter gives a theoretical explanation of the good long-time behaviour of symmetric methods. The results and techniques are largely analogous to those of the previous chapter – the extent of the analogy may indeed be seen as the most surprising feature of this chapter.
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© 2006 Springer
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Hairer, E., Wanner, G., Lubich, C. (2006). Reversible Perturbation Theory and Symmetric Integrators. In: Geometric Numerical Integration. Springer Series in Computational Mathematics, vol 31 . Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30666-8_11
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DOI: https://doi.org/10.1007/3-540-30666-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30663-4
Online ISBN: 978-3-540-30666-5
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